Theoretical investigation of the influence of magnetic and electric fields on the energy spectrum and wave functions of electron in semiconductor spherical layer has been performed. The case of co-directed electric and magnetic fields has been considered. The Schrodinger equation has been solved using the method of expansion for the wave function of electron in the spherical layer under external fields by applying the complete set of wave functions of a quasi-particle in a spherical nanostructure without the external fields. It has been shown that electric and magnetic fields take of the spectrum degeneration with respect to the magnetic quantum number. The external fields rebuild the energy spectrum and deform wave functions of electron. Moreover, their influence on the spherically symmetric state is the largest one. Increasing the magnetic field induction entails a monotonous dependence of the electron energy for the states with <$E m~symbol У~0> and non-monotonous one for the states with <$E m~<<~0>. The ground state of electron is successively formed by the states with <$E m~=~0,~-1,~-2,~...> with increasing the induction of magnetic field. The enhancement of the electric field mainly diminishes the electron energy. The influence of field on the energy and intensities of the 1p-1s intraband transition has been studied. It has been shown that there exists a certain value of the electric field, at which the energy of quantum transition doesn't depend on the magnetic field induction.

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